PetFinder Adoption Final Paper
- Loading data and libraries
Background EDA
We’re using the same dataset as from the midterm assignment. The data comes from Kaggle (https://www.kaggle.com/c/petfinder-adoption-prediction/data) and includs almost 15,000 observations of 23 variables. Each observation is an adoption profile on PetFinder in Malaysia. We chose to keep 9 features, as well as discarding any profile that contained more than one animal, and any animal that did not get adopted in the first 100 days. At the end of these cleaning measures we end up with 8485 observations of the 9 features. Initially we transformed the categorical dependent variable (adoption speed) into a continuous numerical variable. For the sake of this project we are keeping it as a categorical variable for some of our analyses.
As a refresher on the basic features of the dataset we can look at the distribution of the various variables.
First here is our dependent variable Adoption Speed, plotted by number of occurences since it is categorical. 
We can also look at the other numerical features. 
Next we can see the distributions of the categorical variables.
The second is Gender. There are two genders: Male and Female.
The third is MaturitySize. There are four levels, namely Small,Medium, Large, and ExtraLarge.
The fourth is FurLength. There are three levels, namely Short, Medium, and Long.
The fifth is Vaccinated. There are three levels, namely Vaccinated, Unvaccinated, and Not Specified.
After this we did some EDA to see what features affected adoption speed. We initially had a numerical dependent variable so we converted it to a continuous numerical feature. We then ran ANOVAs on a number of the features against the now numerical adoption speed. We discovered that if we disregarded the asumption of equal variance, every feature significantly impacted adoption speed.
#Kaiyuan’s section #SMART QUESTION:What is the probability that a large, female, vaccinated dog would get adopted quickly (adoption speed of 1 or 2).
Yixi’s section
SMART QUESTION: Does animal Type, Gender, MaturitySize, FurLength, and Vaccination status influence the adoption speed significantly, and what is the best model (Logistic Regression, Knn) when considering these variables?
Exhaustive search
##
## The downloaded binary packages are in
## /var/folders/pv/56jgw80j1kd7sdnm17_3lqbh0000gn/T//RtmpVTo6mg/downloaded_packages| Predicted 0 | Predicted 1 | Total | |
|---|---|---|---|
| Actual 0 | 240 | 2530 | 2770 |
| Actual 1 | 207 | 5508 | 5715 |
| Total | 447 | 8038 | 8485 |
## [,1] [,2]
## [1,] 0 0
## [2,] 0 0
#### McFadden
With the McFadden value of 0.033, which is analogous to the coefficient of determination \(R^2\), only about 2% of the variations in y is explained by the explanatory variables in the model.
KNN
Sahara’s section
SMART QUESTION: Can the type of animal be classified from the adoption profile?
Given that the type of animal is a categorical variable this is a classification problem. The first model we can try is a Logistic Regression model. First we need a new clean dataset with the features we want and a renamed target variable for the feature selection.
## 'data.frame': 8485 obs. of 9 variables:
## $ Age : int 3 1 1 4 1 3 12 2 2 3 ...
## $ Gender : Factor w/ 3 levels "1","2","3": 1 1 1 2 1 2 1 2 1 2 ...
## $ MaturitySize : Factor w/ 4 levels "1","2","3","4": 1 2 2 2 2 2 2 2 2 3 ...
## $ FurLength : Factor w/ 3 levels "1","2","3": 1 2 2 1 1 1 3 2 1 3 ...
## $ Vaccinated : Factor w/ 3 levels "1","2","3": 2 3 1 1 2 2 2 2 2 1 ...
## $ PhotoAmt : num 1 2 7 8 3 2 3 6 7 2 ...
## $ VideoAmt : int 0 0 0 0 0 0 0 0 0 0 ...
## $ AdoptionSpeed: Ord.factor w/ 5 levels "0"<"1"<"2"<"3"<..: 3 1 4 3 3 3 2 2 2 2 ...
## $ y : Factor w/ 2 levels "1","2": 2 2 1 1 1 2 2 2 1 2 ...Now we can run the feature selection.
## Age Gender MaturitySize FurLength Vaccinated PhotoAmt VideoAmt AdoptionSpeed
## 1 TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 2 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 3 TRUE FALSE TRUE TRUE TRUE TRUE FALSE TRUE
## 4 TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 5 TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE
## Criterion
## 1 10538
## 2 10540
## 3 10549
## 4 10551
## 5 10583The best model based off this feature selection is every feature except video amount. Now we can make that model.
| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 0.2594 | 0.0822 | 3.154 | 0.0016 |
| Age | -0.0179 | 0.0018 | -10.212 | 0.0000 |
| Gender2 | -0.1801 | 0.0473 | -3.808 | 0.0001 |
| MaturitySize2 | -0.9701 | 0.0589 | -16.464 | 0.0000 |
| MaturitySize3 | -0.7066 | 0.0950 | -7.440 | 0.0000 |
| MaturitySize4 | -0.9954 | 0.4609 | -2.160 | 0.0308 |
| FurLength2 | -0.1634 | 0.0501 | -3.257 | 0.0011 |
| FurLength3 | 0.5550 | 0.0978 | 5.677 | 0.0000 |
| Vaccinated2 | 0.8690 | 0.0528 | 16.446 | 0.0000 |
| Vaccinated3 | -0.1552 | 0.0794 | -1.955 | 0.0506 |
| AdoptionSpeed.L | -0.4891 | 0.0867 | -5.640 | 0.0000 |
| AdoptionSpeed.Q | 0.0333 | 0.0698 | 0.477 | 0.6336 |
| AdoptionSpeed.C | -0.0480 | 0.0479 | -1.002 | 0.3165 |
| PhotoAmt | 0.0566 | 0.0074 | 7.620 | 0.0000 |
There are a number of significant values for these coefficients. But let’s look at other metrics to get a sense of the effectiveness of this model.
##
## Hosmer and Lemeshow goodness of fit (GOF) test
##
## data: datclean$y, fitted(typeLogit)
## X-squared = 8485, df = 8, p-value <2e-16The GOF value is very low which suggests that the model isn’t a great fit. But we can look closer at this with an ROC plot.
## Area under the curve: 0.702The ROC plot confirms that this is not a great model. The AUC value is format(auc(h)), not at our bar of 0.8. Let’s check one more measure.
## fitting null model for pseudo-r2## llh llhNull G2 McFadden r2ML r2CU
## -5.25e+03 -5.82e+03 1.13e+03 9.72e-02 1.25e-01 1.67e-01According to the McFadden score only 10% of the variance in Type is explained by this model, this is incredibly low. Clearly the logistic regression model is not great at classifying type, or type is not decodeable from the profile.
Lets try a KNN model next. First the variables need to be returned to integers to pass into the model and the numerical features need to be scaled. First we’re using all the features and running a search for the optimal K. The search for K went over values 3 - 20.
According to the KNN model with all features included, the best K value is 8 and it produces an accuracy of 0.582.
Let’s try and remove some features. We removed features by logic. For example gender is something that is consistent between types and video amount was removed in the logistic model so we removed it for this test to see if it improved anything. Again we ran through 18 possible K values from 3-20.
Not quite as good as the first model so we’ll stick with that one, all features and a K of 8
However, when we look closer at the predictions we can see that it just over predicted dogs. The balanced accuracy value dropped by a couple percentage points. At the end of all of this we’re basically just above chance in the predictions for both models which leads us to the conclusion that the type of animal can’t be predicted based on the adoption profile.
Alexis’s section
SMART Question: Can puppies/kittens be identified based on their adoption profile?
- To answer the SMART question, let us consider the general problem. There is a categorical dependent variable, and a mixture of numerical and categorical independent variables. A Logistic Regression makes a great deal of sense in this situation. Potentially KNN or classification-tree model.
As 55.05 percent of the pets are puppies, there is a very good balance for our dependent variable.
Logistic Model
- Starting off with a full model, excluding Age as it would perfectly predict 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 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## Fitting algorithm: AIC-glm
## Best Model:
## df deviance
## Null Model 8470 9751
## Full Model 8484 11676
##
## likelihood-ratio test - GLM
##
## data: H0: Null Model vs. H1: Best Fit AIC-glm
## X = 1925, df = 14, p-value <2e-16Summary of Logistic Model Feature Selection
## Type Gender MaturitySize FurLength Vaccinated PhotoAmt VideoAmt AdoptionSpeed
## 1 TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## 2 TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE
## 3 TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
## 4 TRUE FALSE TRUE TRUE TRUE TRUE FALSE TRUE
## 5 TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
## Criterion
## 1 9783
## 2 9785
## 3 9785
## 4 9787
## 5 9804## Type Gender MaturitySize FurLength Vaccinated
## Mode:logical Mode :logical Mode:logical Mode:logical Mode:logical
## TRUE:5 FALSE:2 TRUE:5 TRUE:5 TRUE:5
## TRUE :3
##
##
##
## PhotoAmt VideoAmt AdoptionSpeed Criterion
## Mode :logical Mode :logical Mode:logical Min. :9783
## FALSE:1 FALSE:2 TRUE:5 1st Qu.:9785
## TRUE :4 TRUE :3 Median :9785
## Mean :9789
## 3rd Qu.:9787
## Max. :9804Feature Selection indicates everything except PhotoAmt should be used to generate best logistic model.
Creating Best Logistic Model| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | -0.4796 | 0.0783 | -6.12 | 0.0000 |
| Type2 | -0.5165 | 0.0540 | -9.57 | 0.0000 |
| Gender2 | 0.1164 | 0.0496 | 2.35 | 0.0189 |
| MaturitySize2 | 0.2401 | 0.0604 | 3.97 | 0.0001 |
| MaturitySize3 | -0.8092 | 0.1027 | -7.88 | 0.0000 |
| MaturitySize4 | -1.3693 | 0.5607 | -2.44 | 0.0146 |
| FurLength2 | -0.1202 | 0.0519 | -2.32 | 0.0206 |
| FurLength3 | -1.2685 | 0.1098 | -11.55 | 0.0000 |
| Vaccinated2 | 1.8653 | 0.0565 | 33.03 | 0.0000 |
| Vaccinated3 | 0.2416 | 0.0749 | 3.22 | 0.0013 |
| VideoAmt | 0.2266 | 0.0780 | 2.91 | 0.0037 |
| AdoptionSpeed.L | -0.1137 | 0.0895 | -1.27 | 0.2042 |
| AdoptionSpeed.Q | -0.2980 | 0.0722 | -4.13 | 0.0000 |
| AdoptionSpeed.C | 0.0258 | 0.0506 | 0.51 | 0.6098 |
Confusion Matrix for Logistic Model:
Checking Model Effectiveness
[add analysis]
## Area under the curve: 0.761[add analysis]
Classification Tree
##
## Classification tree:
## rpart(formula = y ~ Vaccinated + AdoptionSpeed, data = datage,
## method = "class", control = list(maxdepth = 20))
##
## Variables actually used in tree construction:
## [1] Vaccinated
##
## Root node error: 3814/8485 = 0.4
##
## n= 8485
##
## CP nsplit rel error xerror xstd
## 1 0.32 0 1.0 1.0 0.01
## 2 0.01 1 0.7 0.7 0.01
## Call:
## rpart(formula = y ~ Type + Gender + MaturitySize + FurLength +
## Vaccinated + PhotoAmt + VideoAmt + AdoptionSpeed, data = datage,
## method = "class", control = list(maxdepth = 20))
## n= 8485
##
## CP nsplit rel error xerror xstd
## 1 0.32 0 1.00 1.00 0.0120
## 2 0.01 1 0.68 0.68 0.0111
##
## Variable importance
## Vaccinated Type AdoptionSpeed
## 81 17 2
##
## Node number 1: 8485 observations, complexity param=0.32
## predicted class=1 expected loss=0.449 P(node) =1
## class counts: 3814 4671
## probabilities: 0.449 0.551
## left son=2 (4546 obs) right son=3 (3939 obs)
## Primary splits:
## Vaccinated splits as LRL, improve=668.0, (0 missing)
## FurLength splits as RRL, improve=127.0, (0 missing)
## MaturitySize splits as RRLL, improve=123.0, (0 missing)
## AdoptionSpeed splits as RRRLL, improve= 26.2, (0 missing)
## PhotoAmt < 3.5 to the left, improve= 10.1, (0 missing)
## Surrogate splits:
## Type splits as LR, agree=0.631, adj=0.205, (0 split)
## AdoptionSpeed splits as RRLLL, agree=0.549, adj=0.029, (0 split)
## PhotoAmt < 9.5 to the left, agree=0.537, adj=0.003, (0 split)
## VideoAmt < 0.5 to the left, agree=0.536, adj=0.001, (0 split)
##
## Node number 2: 4546 observations
## predicted class=0 expected loss=0.366 P(node) =0.536
## class counts: 2883 1663
## probabilities: 0.634 0.366
##
## Node number 3: 3939 observations
## predicted class=1 expected loss=0.236 P(node) =0.464
## class counts: 931 3008
## probabilities: 0.236 0.764Confusion Matrix for Classification Tree
Plot Tree
